Operator product expansion and factorization in the $H_3^+$-WZNW model

TL;DR

This paper provides detailed operator product expansions and factorization formulas in the $H_3^+$-WZNW model, confirming key conjectures and clarifying state roles, thus laying groundwork for string theory on $ADS_3$.

Contribution

It offers precise descriptions of operator product expansions and factorization in the $H_3^+$-WZNW model, verifying conjectures related to string theory on $ADS_3$.

Findings

Verification of the conjecture for space-time current algebra

Clarification of microscopic and macroscopic state roles

Provision of conformal field theory prerequisites for future amplitude studies

Abstract

Precise descriptions are given for the operator product expansion of generic primary fields as well as the factorization of four point functions as sum over intermediate states. The conjecture underlying the recent derivation of the space-time current algebra for string theory on $ADS_3$ by Kutasov and Seiberg is thereby verified. The roles of microscopic and macroscopic states are further clarified. The present work provides the conformal field theory prerequisites for a future study of factorization of amplitudes for string theory on $ADS_3$ as well as operator product expansion in the corresponding conformal field theory on the boundary.